Renormalization group method and canonical perturbation theory

TL;DR

This paper demonstrates that the renormalization group method can be effectively applied to Hamiltonian systems with action-dependent integrable parts, producing results comparable to canonical perturbation theory up to second order.

Contribution

It shows that the renormalization group method yields the same approximate solutions as canonical perturbation theory for specific Hamiltonian systems, establishing a connection between these approaches.

Findings

RG method matches canonical perturbation theory up to second order

Applicable to Hamiltonian systems with linear action dependence

Provides an alternative approach for approximate solutions

Abstract

Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action variables. We show that the renormalization group method gives the same approximate solutions as canonical perturbation theory up to the second order of a small parameter with action-angle coordinates.